find the number of term in an A.P given that its first and last term are a and 37a respectively and that its common difference is 4a
According to your given, the sequence would be
a, 5a, 9a, 13a, 17a,... , 37a
a + (n-1)(4a) = 37a
1 + (n-1)(4) = 37
4n - 4 = 36
4n = 40
n = 10
In an A.P.,Un=a+(n+1)d
First term=a
Common difference=d=4a
Last term In=37a
Un=37a
a+(n-1)(4a)=37a
(n-1)(4a)=36a
n-1=9
n=10
Therefore there are 10 terms in that A.P.
Why did the A.P. go to therapy? Because it had a common difference disorder!
To find the number of terms in an arithmetic progression (A.P.), we can use the formula:
Number of terms = (last term - first term) / common difference + 1
In this case, the first term is "a," the last term is "37a," and the common difference is "4a." Plugging these values into the formula, we get:
Number of terms = (37a - a) / 4a + 1
Simplifying further:
Number of terms = 36a / 4a + 1
Number of terms = 9 + 1
Number of terms = 10
So, there are 10 terms in this arithmetic progression (A.P.).
To find the number of terms in an arithmetic progression (A.P.), we need to know the first term, the last term, and the common difference of the A.P.
In this case, the first term (a) and the last term (37a) are given, as well as the common difference (4a). We can use these values to find the number of terms.
We know that the nth term of an A.P. can be found using the following formula:
nth term = first term + (n - 1) * common difference
For the last term, we have:
37a = a + (n - 1) * 4a
Now, let's solve this equation for 'n':
37a = a + 4a(n - 1)
37a = a + 4an - 4a
37a - a = 4an - 4a
36a = 4a(n - 1)
Divide both sides by 4a:
9 = n - 1
Add 1 to both sides:
n = 10
Therefore, the number of terms in the A.P. is 10.